Yes and no

I hate to kill anything, but if my cats kill a cockroach, who am I to stop what they feel compelled to do. I trust my cats, but I do not trust the cockroach. I don't know how the cockroach thinks, and I don't know what they do. They come out when it's dark, and they don't say hello. It seems they don't want to be seen, and this bothers me. Maybe they are spying on me. Maybe the gecko glued to my window is spying on them, and maybe he is spying on me too. I don't trust anything that won't let me pet them.

Roaches are living creatures who feel pain.

I do not believe there is a real reason to kill roaches. The best solution is to put the roach outside if they happen to get in your house. If they keep coming back, find whatever is letting them in and fix it, whether you use a chemical that keeps them away or simply block it. An infestation is a different matter, but otherwise they can't hurt you.